After you go through Route 110 and enter Mauville City, you battle Wally and gain access to the Electric-type Mauville Gym.
Prepare
Be sure to buy plenty of Parlyz Heals before Mauville Gym. Many of the pokémon here, particularly Wattson's, can cause paralysis.
Prepare your Pokémon
Ground-type pokémon are immune to Electric attacks, making them very useful for this gym. Geodude is a Rock/Ground pokémon that learns its first Ground move, Magnitude, at level 16. In addition, Nincada is Bug/Ground, although it won't learn a Ground attack unless you give it an Everstone and raise it to level 31 (otherwise it would become Ninjask at level 20). If you chose Mudkip as your starter and raised it to level 16, it evolved to the Water/Ground type Marshtomp, making it another good choice for this gym.
Otherwise, you can use Electric or Grass pokémon, which are strong against Electric attacks. Avoid using Flying pokémon or Water pokémon, because they are weak to Electric attacks. However, if you have a Water/Ground pokémon or a Flying/Ground pokémon, it will be immune to Electric attacks.
Some of the trainers here have the Electric/Steel pokémon Magneton and Magnemite. These are weak to Ground, Fighting, and Fire moves, so pokémon like Makuhita and Torchic (for example) could come in handy.
Battle Trainers
In the gym, there are switches and electric barriers. Step on a switch to change which barriers are active.
Near the entrance of the gym, there is Guitarist Kirk. In Ruby and Sapphire, he has a level 18 Electrike and a level 18 Magnemite. In Emerald, he has a level 17 Electrike and a level 17 Voltorb.
In Emerald, Kirk might join Battle Girl Vivian in a Double Battle. She has two level 17 Meditites.
Nearby you find Youngster Ben. In Ruby and Sapphire, he has a level 19 Zigzagoon. In Emerald, he has a level 17 Zigzagoon and a level 17 Gulpin.
There is also Guitarist Shawn. In Ruby and Sapphire, he has three level 17 Voltorbs. In Emerald, he has a level 17 Voltorb and a level 17 Magnemite. In addition, Bug Maniac Angelo might join him in a Double Battle. Angelo has a level 17 Illumise and a level 17 Volbeat. They are Bug-type pokémon, so they are weak to Fire, Flying, and Rock moves.
Wattson
At the north end of the gym, you find Wattson. In Ruby and Sapphire, he has a level 22 Magnemite, a level 20 Voltorb, and a level 23 Magneton. In Emerald, he has a level 20 Voltorb, a level 22 Magneton, a level 20 Electrike, and a level 24 Manectric.
Wattson's Voltorb knows Rollout, which lasts for five turns and causes more and more damage with each turn. It also knows Selfdestruct, which causes it to faint, and causes a lot of damage to your lead pokémon. Be prepared for the possibility that some of your pokémon will faint. You may wish to inflict status ailments on the Voltorb in the hope of avoiding this, or you might want to bring some pokémon with you that you don't mind if they faint.
After Wattson
After you defeat Wattson, he gives you the Dynamo Badge, which lets you use Rock Smash outside of battle. He also gives you TM34 Shock Wave.
After this, you might want to teach Rock Smash to one of your pokémon using the HM that you got from the guy in the house near the Poké Mart here in Mauville City. Then use the west exit of Mauville City to reach Route 117.